If your sheet music doesn't have this "staggered" bass, you need to edit it. The bass should breathe . Use the sustain pedal (damper pedal) to connect the notes, not your finger legato.
Csus2 - G7 - Am - F Csus2 - G7 - Am - F
Could you please provide me with a link to download the sheet music or attach it to this email? I would greatly appreciate it if you could also provide me with any tips or guidance on how to play the song. make it wit chu piano sheet music